NAME

       zgesdd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK,
           INFO)
           ZGESDD

Function/Subroutine Documentation

   subroutine zgesdd (characterJOBZ, integerM, integerN, complex*16, dimension( lda, * )A,
       integerLDA, double precision, dimension( * )S, complex*16, dimension( ldu, * )U,
       integerLDU, complex*16, dimension( ldvt, * )VT, integerLDVT, complex*16, dimension( *
       )WORK, integerLWORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK,
       integerINFO)
       ZGESDD

       Purpose:

            ZGESDD computes the singular value decomposition (SVD) of a complex
            M-by-N matrix A, optionally computing the left and/or right singular
            vectors, by using divide-and-conquer method. The SVD is written

                 A = U * SIGMA * conjugate-transpose(V)

            where SIGMA is an M-by-N matrix which is zero except for its
            min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
            V is an N-by-N unitary matrix.  The diagonal elements of SIGMA
            are the singular values of A; they are real and non-negative, and
            are returned in descending order.  The first min(m,n) columns of
            U and V are the left and right singular vectors of A.

            Note that the routine returns VT = V**H, not V.

            The divide and conquer algorithm makes very mild assumptions about
            floating point arithmetic. It will work on machines with a guard
            digit in add/subtract, or on those binary machines without guard
            digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
            Cray-2. It could conceivably fail on hexadecimal or decimal machines
            without guard digits, but we know of none.

       Parameters:
           JOBZ

                     JOBZ is CHARACTER*1
                     Specifies options for computing all or part of the matrix U:
                     = 'A':  all M columns of U and all N rows of V**H are
                             returned in the arrays U and VT;
                     = 'S':  the first min(M,N) columns of U and the first
                             min(M,N) rows of V**H are returned in the arrays U
                             and VT;
                     = 'O':  If M >= N, the first N columns of U are overwritten
                             in the array A and all rows of V**H are returned in
                             the array VT;
                             otherwise, all columns of U are returned in the
                             array U and the first M rows of V**H are overwritten
                             in the array A;
                     = 'N':  no columns of U or rows of V**H are computed.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, the M-by-N matrix A.
                     On exit,
                     if JOBZ = 'O',  A is overwritten with the first N columns
                                     of U (the left singular vectors, stored
                                     columnwise) if M >= N;
                                     A is overwritten with the first M rows
                                     of V**H (the right singular vectors, stored
                                     rowwise) otherwise.
                     if JOBZ .ne. 'O', the contents of A are destroyed.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           S

                     S is DOUBLE PRECISION array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           U

                     U is COMPLEX*16 array, dimension (LDU,UCOL)
                     UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
                     UCOL = min(M,N) if JOBZ = 'S'.
                     If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
                     unitary matrix U;
                     if JOBZ = 'S', U contains the first min(M,N) columns of U
                     (the left singular vectors, stored columnwise);
                     if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.

           VT

                     VT is COMPLEX*16 array, dimension (LDVT,N)
                     If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
                     N-by-N unitary matrix V**H;
                     if JOBZ = 'S', VT contains the first min(M,N) rows of
                     V**H (the right singular vectors, stored rowwise);
                     if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.

           LDVT

                     LDVT is INTEGER
                     The leading dimension of the array VT.  LDVT >= 1; if
                     JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
                     if JOBZ = 'S', LDVT >= min(M,N).

           WORK

                     WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK. LWORK >= 1.
                     if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
                     if JOBZ = 'O',
                           LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
                     if JOBZ = 'S' or 'A',
                           LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
                     For good performance, LWORK should generally be larger.

                     If LWORK = -1, a workspace query is assumed.  The optimal
                     size for the WORK array is calculated and stored in WORK(1),
                     and no other work except argument checking is performed.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
                     If JOBZ = 'N', LRWORK >= 5*min(M,N).
                     Otherwise,
                     LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)

           IWORK

                     IWORK is INTEGER array, dimension (8*min(M,N))

           INFO

                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  The updating process of DBDSDC did not converge.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Contributors:
           Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
           USA

       Definition at line 222 of file zgesdd.f.

Author

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